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opencv/modules/ml/src/em.cpp

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/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// Intel License Agreement
// For Open Source Computer Vision Library
//
// Copyright( C) 2000, Intel Corporation, all rights reserved.
// Third party copyrights are property of their respective owners.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
//(including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort(including negligence or otherwise) arising in any way out of
// the use of this software, even ifadvised of the possibility of such damage.
//
//M*/
#include "precomp.hpp"
/*
CvEM:
* params.nclusters - number of clusters to cluster samples to.
* means - calculated by the EM algorithm set of gaussians' means.
* log_weight_div_det - auxilary vector that k-th component is equal to
(-2)*ln(weights_k/det(Sigma_k)^0.5),
where <weights_k> is the weight,
<Sigma_k> is the covariation matrice of k-th cluster.
* inv_eigen_values - set of 1*dims matrices, <inv_eigen_values>[k] contains
inversed eigen values of covariation matrice of the k-th cluster.
In the case of <cov_mat_type> == COV_MAT_DIAGONAL,
inv_eigen_values[k] = Sigma_k^(-1).
* covs_rotate_mats - used only if cov_mat_type == COV_MAT_GENERIC, in all the
other cases it is NULL. <covs_rotate_mats>[k] is the orthogonal
matrice, obtained by the SVD-decomposition of Sigma_k.
Both <inv_eigen_values> and <covs_rotate_mats> fields are used for representation of
covariation matrices and simplifying EM calculations.
For fixed k denote
u = covs_rotate_mats[k],
v = inv_eigen_values[k],
w = v^(-1);
if <cov_mat_type> == COV_MAT_GENERIC, then Sigma_k = u w u',
else Sigma_k = w.
Symbol ' means transposition.
*/
CvEMParams::CvEMParams() : nclusters(10), cov_mat_type(1/*CvEM::COV_MAT_DIAGONAL*/),
start_step(0/*CvEM::START_AUTO_STEP*/), probs(0), weights(0), means(0), covs(0)
{
term_crit=cvTermCriteria( CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, 100, FLT_EPSILON );
}
CvEMParams::CvEMParams( int _nclusters, int _cov_mat_type, int _start_step,
CvTermCriteria _term_crit, const CvMat* _probs,
const CvMat* _weights, const CvMat* _means, const CvMat** _covs ) :
nclusters(_nclusters), cov_mat_type(_cov_mat_type), start_step(_start_step),
probs(_probs), weights(_weights), means(_means), covs(_covs), term_crit(_term_crit)
{}
CvEM::CvEM()
{
means = weights = probs = inv_eigen_values = log_weight_div_det = 0;
covs = cov_rotate_mats = 0;
}
CvEM::CvEM( const CvMat* samples, const CvMat* sample_idx,
CvEMParams params, CvMat* labels )
{
means = weights = probs = inv_eigen_values = log_weight_div_det = 0;
covs = cov_rotate_mats = 0;
// just invoke the train() method
train(samples, sample_idx, params, labels);
}
CvEM::~CvEM()
{
clear();
}
void CvEM::clear()
{
int i;
cvReleaseMat( &means );
cvReleaseMat( &weights );
cvReleaseMat( &probs );
cvReleaseMat( &inv_eigen_values );
cvReleaseMat( &log_weight_div_det );
if( covs || cov_rotate_mats )
{
for( i = 0; i < params.nclusters; i++ )
{
if( covs )
cvReleaseMat( &covs[i] );
if( cov_rotate_mats )
cvReleaseMat( &cov_rotate_mats[i] );
}
cvFree( &covs );
cvFree( &cov_rotate_mats );
}
}
void CvEM::read( CvFileStorage* fs, CvFileNode* node )
{
bool ok = false;
CV_FUNCNAME( "CvEM::read" );
__BEGIN__;
clear();
size_t data_size;
CvSeqReader reader;
CvFileNode* em_node = 0;
CvFileNode* tmp_node = 0;
CvSeq* seq = 0;
read_params( fs, node );
em_node = cvGetFileNodeByName( fs, node, "cvEM" );
if( !em_node )
CV_ERROR( CV_StsBadArg, "cvEM tag not found" );
CV_CALL( weights = (CvMat*)cvReadByName( fs, em_node, "weights" ));
CV_CALL( means = (CvMat*)cvReadByName( fs, em_node, "means" ));
CV_CALL( log_weight_div_det = (CvMat*)cvReadByName( fs, em_node, "log_weight_div_det" ));
CV_CALL( inv_eigen_values = (CvMat*)cvReadByName( fs, em_node, "inv_eigen_values" ));
// Size of all the following data
data_size = params.nclusters*sizeof(CvMat*);
CV_CALL( covs = (CvMat**)cvAlloc( data_size ));
memset( covs, 0, data_size );
CV_CALL( tmp_node = cvGetFileNodeByName( fs, em_node, "covs" ));
seq = tmp_node->data.seq;
if( !CV_NODE_IS_SEQ(tmp_node->tag) || seq->total != params.nclusters)
CV_ERROR( CV_StsParseError, "Missing or invalid sequence of covariance matrices" );
CV_CALL( cvStartReadSeq( seq, &reader, 0 ));
for( int i = 0; i < params.nclusters; i++ )
{
CV_CALL( covs[i] = (CvMat*)cvRead( fs, (CvFileNode*)reader.ptr ));
CV_NEXT_SEQ_ELEM( seq->elem_size, reader );
}
CV_CALL( cov_rotate_mats = (CvMat**)cvAlloc( data_size ));
memset( cov_rotate_mats, 0, data_size );
CV_CALL( tmp_node = cvGetFileNodeByName( fs, em_node, "cov_rotate_mats" ));
seq = tmp_node->data.seq;
if( !CV_NODE_IS_SEQ(tmp_node->tag) || seq->total != params.nclusters)
CV_ERROR( CV_StsParseError, "Missing or invalid sequence of covariance matrices" );
CV_CALL( cvStartReadSeq( seq, &reader, 0 ));
for( int i = 0; i < params.nclusters; i++ )
{
CV_CALL( cov_rotate_mats[i] = (CvMat*)cvRead( fs, (CvFileNode*)reader.ptr ));
CV_NEXT_SEQ_ELEM( seq->elem_size, reader );
}
ok = true;
__END__;
if (!ok)
clear();
}
void CvEM::read_params( CvFileStorage *fs, CvFileNode *node)
{
CV_FUNCNAME( "CvEM::read_params");
__BEGIN__;
size_t data_size;
CvEMParams _params;
CvSeqReader reader;
CvFileNode* param_node = 0;
CvFileNode* tmp_node = 0;
CvSeq* seq = 0;
const char * start_step_name = 0;
const char * cov_mat_type_name = 0;
param_node = cvGetFileNodeByName( fs, node, "params" );
if( !param_node )
CV_ERROR( CV_StsBadArg, "params tag not found" );
CV_CALL( start_step_name = cvReadStringByName( fs, param_node, "start_step", 0 ) );
CV_CALL( cov_mat_type_name = cvReadStringByName( fs, param_node, "cov_mat_type", 0 ) );
if( start_step_name )
_params.start_step = strcmp( start_step_name, "START_E_STEP" ) == 0 ? START_E_STEP :
strcmp( start_step_name, "START_M_STEP" ) == 0 ? START_M_STEP :
strcmp( start_step_name, "START_AUTO_STEP" ) == 0 ? START_AUTO_STEP : 0;
else
CV_CALL( _params.start_step = cvReadIntByName( fs, param_node, "start_step", -1 ) );
if( cov_mat_type_name )
_params.cov_mat_type = strcmp( cov_mat_type_name, "COV_MAT_SPHERICAL" ) == 0 ? COV_MAT_SPHERICAL :
strcmp( cov_mat_type_name, "COV_MAT_DIAGONAL" ) == 0 ? COV_MAT_DIAGONAL :
strcmp( cov_mat_type_name, "COV_MAT_GENERIC" ) == 0 ? COV_MAT_GENERIC : 0;
else
CV_CALL( _params.cov_mat_type = cvReadIntByName( fs, param_node, "cov_mat_type", -1) );
CV_CALL( _params.nclusters = cvReadIntByName( fs, param_node, "nclusters", -1 ));
CV_CALL( _params.weights = (CvMat*)cvReadByName( fs, param_node, "weights" ));
CV_CALL( _params.means = (CvMat*)cvReadByName( fs, param_node, "means" ));
data_size = _params.nclusters*sizeof(CvMat*);
CV_CALL( _params.covs = (const CvMat**)cvAlloc( data_size ));
memset( _params.covs, 0, data_size );
CV_CALL( tmp_node = cvGetFileNodeByName( fs, param_node, "covs" ));
seq = tmp_node->data.seq;
if( !CV_NODE_IS_SEQ(tmp_node->tag) || seq->total != _params.nclusters)
CV_ERROR( CV_StsParseError, "Missing or invalid sequence of covariance matrices" );
CV_CALL( cvStartReadSeq( seq, &reader, 0 ));
for( int i = 0; i < _params.nclusters; i++ )
{
CV_CALL( _params.covs[i] = (CvMat*)cvRead( fs, (CvFileNode*)reader.ptr ));
CV_NEXT_SEQ_ELEM( seq->elem_size, reader );
}
params = _params;
__END__;
}
void CvEM::write_params( CvFileStorage* fs ) const
{
CV_FUNCNAME( "CvEM::write_params" );
__BEGIN__;
const char* cov_mat_type_name =
(params.cov_mat_type == COV_MAT_SPHERICAL) ? "COV_MAT_SPHERICAL" :
(params.cov_mat_type == COV_MAT_DIAGONAL) ? "COV_MAT_DIAGONAL" :
(params.cov_mat_type == COV_MAT_GENERIC) ? "COV_MAT_GENERIC" : 0;
const char* start_step_name =
(params.start_step == START_E_STEP) ? "START_E_STEP" :
(params.start_step == START_M_STEP) ? "START_M_STEP" :
(params.start_step == START_AUTO_STEP) ? "START_AUTO_STEP" : 0;
CV_CALL( cvStartWriteStruct( fs, "params", CV_NODE_MAP ) );
if( cov_mat_type_name )
{
CV_CALL( cvWriteString( fs, "cov_mat_type", cov_mat_type_name) );
}
else
{
CV_CALL( cvWriteInt( fs, "cov_mat_type", params.cov_mat_type ) );
}
if( start_step_name )
{
CV_CALL( cvWriteString( fs, "start_step", start_step_name) );
}
else
{
CV_CALL( cvWriteInt( fs, "cov_mat_type", params.start_step ) );
}
CV_CALL( cvWriteInt( fs, "nclusters", params.nclusters ));
CV_CALL( cvWrite( fs, "weights", weights ));
CV_CALL( cvWrite( fs, "means", means ));
CV_CALL( cvStartWriteStruct( fs, "covs", CV_NODE_SEQ ));
for( int i = 0; i < params.nclusters; i++ )
CV_CALL( cvWrite( fs, NULL, covs[i] ));
CV_CALL( cvEndWriteStruct( fs ) );
// Close params struct
CV_CALL( cvEndWriteStruct( fs ) );
__END__;
}
void CvEM::write( CvFileStorage* fs, const char* name ) const
{
CV_FUNCNAME( "CvEM::write" );
__BEGIN__;
CV_CALL( cvStartWriteStruct( fs, name, CV_NODE_MAP, CV_TYPE_NAME_ML_EM ) );
write_params(fs);
CV_CALL( cvStartWriteStruct( fs, "cvEM", CV_NODE_MAP ) );
CV_CALL( cvWrite( fs, "means", means ) );
CV_CALL( cvWrite( fs, "weights", weights ) );
CV_CALL( cvWrite( fs, "log_weight_div_det", log_weight_div_det ) );
CV_CALL( cvWrite( fs, "inv_eigen_values", inv_eigen_values ) );
CV_CALL( cvStartWriteStruct( fs, "covs", CV_NODE_SEQ ));
for( int i = 0; i < params.nclusters; i++ )
CV_CALL( cvWrite( fs, NULL, covs[i] ));
CV_CALL( cvEndWriteStruct( fs ));
CV_CALL( cvStartWriteStruct( fs, "cov_rotate_mats", CV_NODE_SEQ ));
for( int i = 0; i < params.nclusters; i++ )
CV_CALL( cvWrite( fs, NULL, cov_rotate_mats[i] ));
CV_CALL( cvEndWriteStruct( fs ) );
// close cvEM
CV_CALL( cvEndWriteStruct( fs ) );
// close top level
CV_CALL( cvEndWriteStruct( fs ) );
__END__;
}
void CvEM::set_params( const CvEMParams& _params, const CvVectors& train_data )
{
CV_FUNCNAME( "CvEM::set_params" );
__BEGIN__;
int k;
params = _params;
params.term_crit = cvCheckTermCriteria( params.term_crit, 1e-6, 10000 );
if( params.cov_mat_type != COV_MAT_SPHERICAL &&
params.cov_mat_type != COV_MAT_DIAGONAL &&
params.cov_mat_type != COV_MAT_GENERIC )
CV_ERROR( CV_StsBadArg, "Unknown covariation matrix type" );
switch( params.start_step )
{
case START_M_STEP:
if( !params.probs )
CV_ERROR( CV_StsNullPtr, "Probabilities must be specified when EM algorithm starts with M-step" );
break;
case START_E_STEP:
if( !params.means )
CV_ERROR( CV_StsNullPtr, "Mean's must be specified when EM algorithm starts with E-step" );
break;
case START_AUTO_STEP:
break;
default:
CV_ERROR( CV_StsBadArg, "Unknown start_step" );
}
if( params.nclusters < 1 )
CV_ERROR( CV_StsOutOfRange, "The number of clusters (mixtures) should be > 0" );
if( params.probs )
{
const CvMat* p = params.probs;
if( !CV_IS_MAT(p) ||
(CV_MAT_TYPE(p->type) != CV_32FC1 &&
CV_MAT_TYPE(p->type) != CV_64FC1) ||
p->rows != train_data.count ||
p->cols != params.nclusters )
CV_ERROR( CV_StsBadArg, "The array of probabilities must be a valid "
"floating-point matrix (CvMat) of 'nsamples' x 'nclusters' size" );
}
if( params.means )
{
const CvMat* m = params.means;
if( !CV_IS_MAT(m) ||
(CV_MAT_TYPE(m->type) != CV_32FC1 &&
CV_MAT_TYPE(m->type) != CV_64FC1) ||
m->rows != params.nclusters ||
m->cols != train_data.dims )
CV_ERROR( CV_StsBadArg, "The array of mean's must be a valid "
"floating-point matrix (CvMat) of 'nsamples' x 'dims' size" );
}
if( params.weights )
{
const CvMat* w = params.weights;
if( !CV_IS_MAT(w) ||
(CV_MAT_TYPE(w->type) != CV_32FC1 &&
CV_MAT_TYPE(w->type) != CV_64FC1) ||
(w->rows != 1 && w->cols != 1) ||
w->rows + w->cols - 1 != params.nclusters )
CV_ERROR( CV_StsBadArg, "The array of weights must be a valid "
"1d floating-point vector (CvMat) of 'nclusters' elements" );
}
if( params.covs )
for( k = 0; k < params.nclusters; k++ )
{
const CvMat* cov = params.covs[k];
if( !CV_IS_MAT(cov) ||
(CV_MAT_TYPE(cov->type) != CV_32FC1 &&
CV_MAT_TYPE(cov->type) != CV_64FC1) ||
cov->rows != cov->cols || cov->cols != train_data.dims )
CV_ERROR( CV_StsBadArg,
"Each of covariation matrices must be a valid square "
"floating-point matrix (CvMat) of 'dims' x 'dims'" );
}
__END__;
}
/****************************************************************************************/
double CvEM::calcLikelihood( const cv::Mat &input_sample ) const
{
const CvMat _input_sample = input_sample;
const CvMat* _sample = &_input_sample ;
float* sample_data = 0;
int cov_mat_type = params.cov_mat_type;
int i, dims = means->cols;
int nclusters = params.nclusters;
cvPreparePredictData( _sample, dims, 0, params.nclusters, 0, &sample_data );
// allocate memory and initializing headers for calculating
cv::AutoBuffer<double> buffer(nclusters + dims);
CvMat expo = cvMat(1, nclusters, CV_64F, &buffer[0] );
CvMat diff = cvMat(1, dims, CV_64F, &buffer[nclusters] );
// calculate the probabilities
for( int k = 0; k < nclusters; k++ )
{
const double* mean_k = (const double*)(means->data.ptr + means->step*k);
const double* w = (const double*)(inv_eigen_values->data.ptr + inv_eigen_values->step*k);
double cur = log_weight_div_det->data.db[k];
CvMat* u = cov_rotate_mats[k];
// cov = u w u' --> cov^(-1) = u w^(-1) u'
if( cov_mat_type == COV_MAT_SPHERICAL )
{
double w0 = w[0];
for( i = 0; i < dims; i++ )
{
double val = sample_data[i] - mean_k[i];
cur += val*val*w0;
}
}
else
{
for( i = 0; i < dims; i++ )
diff.data.db[i] = sample_data[i] - mean_k[i];
if( cov_mat_type == COV_MAT_GENERIC )
cvGEMM( &diff, u, 1, 0, 0, &diff, CV_GEMM_B_T );
for( i = 0; i < dims; i++ )
{
double val = diff.data.db[i];
cur += val*val*w[i];
}
}
expo.data.db[k] = cur;
}
// probability = (2*pi)^(-dims/2)*exp( -0.5 * cur )
cvConvertScale( &expo, &expo, -0.5 );
double factor = -double(dims)/2.0 * log(2.0*CV_PI);
cvAndS( &expo, cvScalar(factor), &expo );
// Calculate the log-likelihood of the given sample -
// see Alex Smola's blog http://blog.smola.org/page/2 for
// details on the log-sum-exp trick
double mini,maxi,retval;
cvMinMaxLoc( &expo, &mini, &maxi, 0, 0 );
CvMat *flp = cvCloneMat(&expo);
cvSubS( &expo, cvScalar(maxi), flp);
cvExp( flp, flp );
CvScalar ss = cvSum( flp );
retval = log(ss.val[0]) + maxi;
cvReleaseMat(&flp);
if( sample_data != _sample->data.fl )
cvFree( &sample_data );
return retval;
}
/****************************************************************************************/
float
CvEM::predict( const CvMat* _sample, CvMat* _probs ) const
{
float* sample_data = 0;
int cls = 0;
int cov_mat_type = params.cov_mat_type;
double opt = FLT_MAX;
int i, dims = means->cols;
int nclusters = params.nclusters;
cvPreparePredictData( _sample, dims, 0, params.nclusters, _probs, &sample_data );
// allocate memory and initializing headers for calculating
cv::AutoBuffer<double> buffer(nclusters + dims);
CvMat expo = cvMat(1, nclusters, CV_64F, &buffer[0] );
CvMat diff = cvMat(1, dims, CV_64F, &buffer[nclusters] );
// calculate the probabilities
for( int k = 0; k < nclusters; k++ )
{
const double* mean_k = (const double*)(means->data.ptr + means->step*k);
const double* w = (const double*)(inv_eigen_values->data.ptr + inv_eigen_values->step*k);
double cur = log_weight_div_det->data.db[k];
CvMat* u = cov_rotate_mats[k];
// cov = u w u' --> cov^(-1) = u w^(-1) u'
if( cov_mat_type == COV_MAT_SPHERICAL )
{
double w0 = w[0];
for( i = 0; i < dims; i++ )
{
double val = sample_data[i] - mean_k[i];
cur += val*val*w0;
}
}
else
{
for( i = 0; i < dims; i++ )
diff.data.db[i] = sample_data[i] - mean_k[i];
if( cov_mat_type == COV_MAT_GENERIC )
cvGEMM( &diff, u, 1, 0, 0, &diff, CV_GEMM_B_T );
for( i = 0; i < dims; i++ )
{
double val = diff.data.db[i];
cur += val*val*w[i];
}
}
expo.data.db[k] = cur;
if( cur < opt )
{
cls = k;
opt = cur;
}
}
// probability = (2*pi)^(-dims/2)*exp( -0.5 * cur )
cvConvertScale( &expo, &expo, -0.5 );
double factor = -double(dims)/2.0 * log(2.0*CV_PI);
cvAndS( &expo, cvScalar(factor), &expo );
// Calculate the posterior probability of each component
// given the sample data.
if( _probs )
{
cvExp( &expo, &expo );
if( _probs->cols == 1 )
cvReshape( &expo, &expo, 0, nclusters );
cvConvertScale( &expo, _probs, 1./cvSum( &expo ).val[0] );
}
if( sample_data != _sample->data.fl )
cvFree( &sample_data );
return (float)cls;
}
bool CvEM::train( const CvMat* _samples, const CvMat* _sample_idx,
CvEMParams _params, CvMat* labels )
{
bool result = false;
CvVectors train_data;
CvMat* sample_idx = 0;
train_data.data.fl = 0;
train_data.count = 0;
CV_FUNCNAME("cvEM");
__BEGIN__;
int i, nsamples, nclusters, dims;
clear();
CV_CALL( cvPrepareTrainData( "cvEM",
_samples, CV_ROW_SAMPLE, 0, CV_VAR_CATEGORICAL,
0, _sample_idx, false, (const float***)&train_data.data.fl,
&train_data.count, &train_data.dims, &train_data.dims,
0, 0, 0, &sample_idx ));
CV_CALL( set_params( _params, train_data ));
nsamples = train_data.count;
nclusters = params.nclusters;
dims = train_data.dims;
if( labels && (!CV_IS_MAT(labels) || CV_MAT_TYPE(labels->type) != CV_32SC1 ||
(labels->cols != 1 && labels->rows != 1) || labels->cols + labels->rows - 1 != nsamples ))
CV_ERROR( CV_StsBadArg,
"labels array (when passed) must be a valid 1d integer vector of <sample_count> elements" );
if( nsamples <= nclusters )
CV_ERROR( CV_StsOutOfRange,
"The number of samples should be greater than the number of clusters" );
CV_CALL( log_weight_div_det = cvCreateMat( 1, nclusters, CV_64FC1 ));
CV_CALL( probs = cvCreateMat( nsamples, nclusters, CV_64FC1 ));
CV_CALL( means = cvCreateMat( nclusters, dims, CV_64FC1 ));
CV_CALL( weights = cvCreateMat( 1, nclusters, CV_64FC1 ));
CV_CALL( inv_eigen_values = cvCreateMat( nclusters,
params.cov_mat_type == COV_MAT_SPHERICAL ? 1 : dims, CV_64FC1 ));
CV_CALL( covs = (CvMat**)cvAlloc( nclusters * sizeof(*covs) ));
CV_CALL( cov_rotate_mats = (CvMat**)cvAlloc( nclusters * sizeof(cov_rotate_mats[0]) ));
for( i = 0; i < nclusters; i++ )
{
CV_CALL( covs[i] = cvCreateMat( dims, dims, CV_64FC1 ));
CV_CALL( cov_rotate_mats[i] = cvCreateMat( dims, dims, CV_64FC1 ));
cvZero( cov_rotate_mats[i] );
}
init_em( train_data );
log_likelihood = run_em( train_data );
if( log_likelihood <= -DBL_MAX/10000. )
EXIT;
if( labels )
{
if( nclusters == 1 )
cvZero( labels );
else
{
CvMat sample = cvMat( 1, dims, CV_32F );
CvMat prob = cvMat( 1, nclusters, CV_64F );
int lstep = CV_IS_MAT_CONT(labels->type) ? 1 : labels->step/sizeof(int);
for( i = 0; i < nsamples; i++ )
{
int idx = sample_idx ? sample_idx->data.i[i] : i;
sample.data.ptr = _samples->data.ptr + _samples->step*idx;
prob.data.ptr = probs->data.ptr + probs->step*i;
labels->data.i[i*lstep] = cvRound(predict(&sample, &prob));
}
}
}
result = true;
__END__;
if( sample_idx != _sample_idx )
cvReleaseMat( &sample_idx );
cvFree( &train_data.data.ptr );
return result;
}
void CvEM::init_em( const CvVectors& train_data )
{
CvMat *w = 0, *u = 0, *tcov = 0;
CV_FUNCNAME( "CvEM::init_em" );
__BEGIN__;
double maxval = 0;
int i, force_symm_plus = 0;
int nclusters = params.nclusters, nsamples = train_data.count, dims = train_data.dims;
if( params.start_step == START_AUTO_STEP || nclusters == 1 || nclusters == nsamples )
init_auto( train_data );
else if( params.start_step == START_M_STEP )
{
for( i = 0; i < nsamples; i++ )
{
CvMat prob;
cvGetRow( params.probs, &prob, i );
cvMaxS( &prob, 0., &prob );
cvMinMaxLoc( &prob, 0, &maxval );
if( maxval < FLT_EPSILON )
cvSet( &prob, cvScalar(1./nclusters) );
else
cvNormalize( &prob, &prob, 1., 0, CV_L1 );
}
EXIT; // do not preprocess covariation matrices,
// as in this case they are initialized at the first iteration of EM
}
else
{
CV_ASSERT( params.start_step == START_E_STEP && params.means );
if( params.weights && params.covs )
{
cvConvert( params.means, means );
cvReshape( weights, weights, 1, params.weights->rows );
cvConvert( params.weights, weights );
cvReshape( weights, weights, 1, 1 );
cvMaxS( weights, 0., weights );
cvMinMaxLoc( weights, 0, &maxval );
if( maxval < FLT_EPSILON )
cvSet( weights, cvScalar(1./nclusters) );
cvNormalize( weights, weights, 1., 0, CV_L1 );
for( i = 0; i < nclusters; i++ )
CV_CALL( cvConvert( params.covs[i], covs[i] ));
force_symm_plus = 1;
}
else
init_auto( train_data );
}
CV_CALL( tcov = cvCreateMat( dims, dims, CV_64FC1 ));
CV_CALL( w = cvCreateMat( dims, dims, CV_64FC1 ));
if( params.cov_mat_type != COV_MAT_SPHERICAL )
CV_CALL( u = cvCreateMat( dims, dims, CV_64FC1 ));
for( i = 0; i < nclusters; i++ )
{
if( force_symm_plus )
{
cvTranspose( covs[i], tcov );
cvAddWeighted( covs[i], 0.5, tcov, 0.5, 0, tcov );
}
else
cvCopy( covs[i], tcov );
cvSVD( tcov, w, u, 0, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T );
if( params.cov_mat_type == COV_MAT_SPHERICAL )
cvSetIdentity( covs[i], cvScalar(cvTrace(w).val[0]/dims) );
/*else if( params.cov_mat_type == COV_MAT_DIAGONAL )
cvCopy( w, covs[i] );*/
else
{
// generic case: covs[i] = (u')'*max(w,0)*u'
cvGEMM( u, w, 1, 0, 0, tcov, CV_GEMM_A_T );
cvGEMM( tcov, u, 1, 0, 0, covs[i], 0 );
}
}
__END__;
cvReleaseMat( &w );
cvReleaseMat( &u );
cvReleaseMat( &tcov );
}
void CvEM::init_auto( const CvVectors& train_data )
{
CvMat* hdr = 0;
const void** vec = 0;
CvMat* class_ranges = 0;
CvMat* labels = 0;
CV_FUNCNAME( "CvEM::init_auto" );
__BEGIN__;
int nclusters = params.nclusters, nsamples = train_data.count, dims = train_data.dims;
int i, j;
if( nclusters == nsamples )
{
CvMat src = cvMat( 1, dims, CV_32F );
CvMat dst = cvMat( 1, dims, CV_64F );
for( i = 0; i < nsamples; i++ )
{
src.data.ptr = train_data.data.ptr[i];
dst.data.ptr = means->data.ptr + means->step*i;
cvConvert( &src, &dst );
cvZero( covs[i] );
cvSetIdentity( cov_rotate_mats[i] );
}
cvSetIdentity( probs );
cvSet( weights, cvScalar(1./nclusters) );
}
else
{
int max_count = 0;
CV_CALL( class_ranges = cvCreateMat( 1, nclusters+1, CV_32SC1 ));
if( nclusters > 1 )
{
CV_CALL( labels = cvCreateMat( 1, nsamples, CV_32SC1 ));
// Not fully executed in case means are already given
kmeans( train_data, nclusters, labels, cvTermCriteria( CV_TERMCRIT_ITER,
params.means ? 1 : 10, 0.5 ), params.means );
CV_CALL( cvSortSamplesByClasses( (const float**)train_data.data.fl,
labels, class_ranges->data.i ));
}
else
{
class_ranges->data.i[0] = 0;
class_ranges->data.i[1] = nsamples;
}
for( i = 0; i < nclusters; i++ )
{
int left = class_ranges->data.i[i], right = class_ranges->data.i[i+1];
max_count = MAX( max_count, right - left );
}
CV_CALL( hdr = (CvMat*)cvAlloc( max_count*sizeof(hdr[0]) ));
CV_CALL( vec = (const void**)cvAlloc( max_count*sizeof(vec[0]) ));
hdr[0] = cvMat( 1, dims, CV_32F );
for( i = 0; i < max_count; i++ )
{
vec[i] = hdr + i;
hdr[i] = hdr[0];
}
for( i = 0; i < nclusters; i++ )
{
int left = class_ranges->data.i[i], right = class_ranges->data.i[i+1];
int cluster_size = right - left;
CvMat avg;
if( cluster_size <= 0 )
continue;
for( j = left; j < right; j++ )
hdr[j - left].data.fl = train_data.data.fl[j];
CV_CALL( cvGetRow( means, &avg, i ));
CV_CALL( cvCalcCovarMatrix( vec, cluster_size, covs[i],
&avg, CV_COVAR_NORMAL | CV_COVAR_SCALE ));
weights->data.db[i] = (double)cluster_size/(double)nsamples;
}
}
__END__;
cvReleaseMat( &class_ranges );
cvReleaseMat( &labels );
cvFree( &hdr );
cvFree( &vec );
}
void CvEM::kmeans( const CvVectors& train_data, int nclusters, CvMat* labels,
CvTermCriteria termcrit, const CvMat* /*centers0*/ )
{
int i, nsamples = train_data.count, dims = train_data.dims;
cv::Ptr<CvMat> temp_mat = cvCreateMat(nsamples, dims, CV_32F);
for( i = 0; i < nsamples; i++ )
memcpy( temp_mat->data.ptr + temp_mat->step*i, train_data.data.fl[i], dims*sizeof(float));
cvKMeans2(temp_mat, nclusters, labels, termcrit, 10);
}
/****************************************************************************************/
/* log_weight_div_det[k] = -2*log(weights_k) + log(det(Sigma_k)))
covs[k] = cov_rotate_mats[k] * cov_eigen_values[k] * (cov_rotate_mats[k])'
cov_rotate_mats[k] are orthogonal matrices of eigenvectors and
cov_eigen_values[k] are diagonal matrices (represented by 1D vectors) of eigen values.
The <alpha_ik> is the probability of the vector x_i to belong to the k-th cluster:
<alpha_ik> ~ weights_k * exp{ -0.5[ln(det(Sigma_k)) + (x_i - mu_k)' Sigma_k^(-1) (x_i - mu_k)] }
We calculate these probabilities here by the equivalent formulae:
Denote
S_ik = -0.5(log(det(Sigma_k)) + (x_i - mu_k)' Sigma_k^(-1) (x_i - mu_k)) + log(weights_k),
M_i = max_k S_ik = S_qi, so that the q-th class is the one where maximum reaches. Then
alpha_ik = exp{ S_ik - M_i } / ( 1 + sum_j!=q exp{ S_ji - M_i })
*/
double CvEM::run_em( const CvVectors& train_data )
{
CvMat* centered_sample = 0;
CvMat* covs_item = 0;
CvMat* log_det = 0;
CvMat* log_weights = 0;
CvMat* cov_eigen_values = 0;
CvMat* samples = 0;
CvMat* sum_probs = 0;
log_likelihood = -DBL_MAX;
CV_FUNCNAME( "CvEM::run_em" );
__BEGIN__;
int nsamples = train_data.count, dims = train_data.dims, nclusters = params.nclusters;
double min_variation = FLT_EPSILON;
double min_det_value = MAX( DBL_MIN, pow( min_variation, dims ));
double _log_likelihood = -DBL_MAX;
int start_step = params.start_step;
double sum_max_val;
int i, j, k, n;
int is_general = 0, is_diagonal = 0, is_spherical = 0;
double prev_log_likelihood = -DBL_MAX / 1000., det, d;
CvMat whdr, iwhdr, diag, *w, *iw;
double* w_data;
double* sp_data;
if( nclusters == 1 )
{
double log_weight;
CV_CALL( cvSet( probs, cvScalar(1.)) );
if( params.cov_mat_type == COV_MAT_SPHERICAL )
{
d = cvTrace(*covs).val[0]/dims;
d = MAX( d, FLT_EPSILON );
inv_eigen_values->data.db[0] = 1./d;
log_weight = pow( d, dims*0.5 );
}
else
{
w_data = inv_eigen_values->data.db;
if( params.cov_mat_type == COV_MAT_GENERIC )
cvSVD( *covs, inv_eigen_values, *cov_rotate_mats, 0, CV_SVD_U_T );
else
cvTranspose( cvGetDiag(*covs, &diag), inv_eigen_values );
cvMaxS( inv_eigen_values, FLT_EPSILON, inv_eigen_values );
for( j = 0, det = 1.; j < dims; j++ )
det *= w_data[j];
log_weight = sqrt(det);
cvDiv( 0, inv_eigen_values, inv_eigen_values );
}
log_weight_div_det->data.db[0] = -2*log(weights->data.db[0]/log_weight);
log_likelihood = DBL_MAX/1000.;
EXIT;
}
if( params.cov_mat_type == COV_MAT_GENERIC )
is_general = 1;
else if( params.cov_mat_type == COV_MAT_DIAGONAL )
is_diagonal = 1;
else if( params.cov_mat_type == COV_MAT_SPHERICAL )
is_spherical = 1;
/* In the case of <cov_mat_type> == COV_MAT_DIAGONAL, the k-th row of cov_eigen_values
contains the diagonal elements (variations). In the case of
<cov_mat_type> == COV_MAT_SPHERICAL - the 0-ths elements of the vectors cov_eigen_values[k]
are to be equal to the mean of the variations over all the dimensions. */
CV_CALL( log_det = cvCreateMat( 1, nclusters, CV_64FC1 ));
CV_CALL( log_weights = cvCreateMat( 1, nclusters, CV_64FC1 ));
CV_CALL( covs_item = cvCreateMat( dims, dims, CV_64FC1 ));
CV_CALL( centered_sample = cvCreateMat( 1, dims, CV_64FC1 ));
CV_CALL( cov_eigen_values = cvCreateMat( inv_eigen_values->rows, inv_eigen_values->cols, CV_64FC1 ));
CV_CALL( samples = cvCreateMat( nsamples, dims, CV_64FC1 ));
CV_CALL( sum_probs = cvCreateMat( 1, nclusters, CV_64FC1 ));
sp_data = sum_probs->data.db;
// copy the training data into double-precision matrix
for( i = 0; i < nsamples; i++ )
{
const float* src = train_data.data.fl[i];
double* dst = (double*)(samples->data.ptr + samples->step*i);
for( j = 0; j < dims; j++ )
dst[j] = src[j];
}
if( start_step != START_M_STEP )
{
for( k = 0; k < nclusters; k++ )
{
if( is_general || is_diagonal )
{
w = cvGetRow( cov_eigen_values, &whdr, k );
if( is_general )
cvSVD( covs[k], w, cov_rotate_mats[k], 0, CV_SVD_U_T );
else
cvTranspose( cvGetDiag( covs[k], &diag ), w );
w_data = w->data.db;
for( j = 0, det = 0.; j < dims; j++ )
det += std::log(w_data[j]);
if( det < std::log(min_det_value) )
{
if( start_step == START_AUTO_STEP )
det = std::log(min_det_value);
else
EXIT;
}
log_det->data.db[k] = det;
}
else // spherical
{
d = cvTrace(covs[k]).val[0]/(double)dims;
if( d < min_variation )
{
if( start_step == START_AUTO_STEP )
d = min_variation;
else
EXIT;
}
cov_eigen_values->data.db[k] = d;
log_det->data.db[k] = d;
}
}
if( is_spherical )
{
cvLog( log_det, log_det );
cvScale( log_det, log_det, dims );
}
}
for( n = 0; n < params.term_crit.max_iter; n++ )
{
if( n > 0 || start_step != START_M_STEP )
{
// e-step: compute probs_ik from means_k, covs_k and weights_k.
CV_CALL(cvLog( weights, log_weights ));
sum_max_val = 0.;
// S_ik = -0.5[log(det(Sigma_k)) + (x_i - mu_k)' Sigma_k^(-1) (x_i - mu_k)] + log(weights_k)
for( k = 0; k < nclusters; k++ )
{
CvMat* u = cov_rotate_mats[k];
const double* mean = (double*)(means->data.ptr + means->step*k);
w = cvGetRow( cov_eigen_values, &whdr, k );
iw = cvGetRow( inv_eigen_values, &iwhdr, k );
cvDiv( 0, w, iw );
w_data = (double*)(inv_eigen_values->data.ptr + inv_eigen_values->step*k);
for( i = 0; i < nsamples; i++ )
{
double *csample = centered_sample->data.db, p = log_det->data.db[k];
const double* sample = (double*)(samples->data.ptr + samples->step*i);
double* pp = (double*)(probs->data.ptr + probs->step*i);
for( j = 0; j < dims; j++ )
csample[j] = sample[j] - mean[j];
if( is_general )
cvGEMM( centered_sample, u, 1, 0, 0, centered_sample, CV_GEMM_B_T );
for( j = 0; j < dims; j++ )
p += csample[j]*csample[j]*w_data[is_spherical ? 0 : j];
//pp[k] = -0.5*p + log_weights->data.db[k];
pp[k] = -0.5*(p+CV_LOG2PI * (double)dims) + log_weights->data.db[k];
// S_ik <- S_ik - max_j S_ij
if( k == nclusters - 1 )
{
double max_val = pp[0];
for( j = 1; j < nclusters; j++ )
max_val = MAX( max_val, pp[j] );
sum_max_val += max_val;
for( j = 0; j < nclusters; j++ )
pp[j] -= max_val;
}
}
}
CV_CALL(cvExp( probs, probs )); // exp( S_ik )
cvZero( sum_probs );
// alpha_ik = exp( S_ik ) / sum_j exp( S_ij ),
// log_likelihood = sum_i log (sum_j exp(S_ij))
for( i = 0, _log_likelihood = 0; i < nsamples; i++ )
{
double* pp = (double*)(probs->data.ptr + probs->step*i), sum = 0;
for( j = 0; j < nclusters; j++ )
sum += pp[j];
sum = 1./MAX( sum, DBL_EPSILON );
for( j = 0; j < nclusters; j++ )
{
double p = pp[j] *= sum;
sp_data[j] += p;
}
_log_likelihood -= log( sum );
}
_log_likelihood+=sum_max_val;
// Check termination criteria. Use the same termination criteria as it is used in MATLAB
log_likelihood_delta = _log_likelihood - prev_log_likelihood;
// if( n>0 )
// fprintf(stderr, "iter=%d, ll=%0.5f (delta=%0.5f, goal=%0.5f)\n",
// n, _log_likelihood, delta, params.term_crit.epsilon * fabs( _log_likelihood));
if ( log_likelihood_delta > 0 && log_likelihood_delta < params.term_crit.epsilon * std::fabs( _log_likelihood) )
break;
prev_log_likelihood = _log_likelihood;
}
// m-step: update means_k, covs_k and weights_k from probs_ik
cvGEMM( probs, samples, 1, 0, 0, means, CV_GEMM_A_T );
for( k = 0; k < nclusters; k++ )
{
double sum = sp_data[k], inv_sum = 1./sum;
CvMat* cov = covs[k], _mean, _sample;
w = cvGetRow( cov_eigen_values, &whdr, k );
w_data = w->data.db;
cvGetRow( means, &_mean, k );
cvGetRow( samples, &_sample, k );
// update weights_k
weights->data.db[k] = sum;
// update means_k
cvScale( &_mean, &_mean, inv_sum );
// compute covs_k
cvZero( cov );
cvZero( w );
for( i = 0; i < nsamples; i++ )
{
double p = probs->data.db[i*nclusters + k]*inv_sum;
_sample.data.db = (double*)(samples->data.ptr + samples->step*i);
if( is_general )
{
cvMulTransposed( &_sample, covs_item, 1, &_mean );
cvScaleAdd( covs_item, cvRealScalar(p), cov, cov );
}
else
for( j = 0; j < dims; j++ )
{
double val = _sample.data.db[j] - _mean.data.db[j];
w_data[is_spherical ? 0 : j] += p*val*val;
}
}
if( is_spherical )
{
d = w_data[0]/(double)dims;
d = MAX( d, min_variation );
w->data.db[0] = d;
log_det->data.db[k] = d;
}
else
{
// Det. of general NxN cov. matrix is the prod. of the eig. vals
if( is_general )
cvSVD( cov, w, cov_rotate_mats[k], 0, CV_SVD_U_T );
cvMaxS( w, min_variation, w );
for( j = 0, det = 0.; j < dims; j++ )
det += std::log( w_data[j] );
log_det->data.db[k] = det;
}
}
cvConvertScale( weights, weights, 1./(double)nsamples, 0 );
cvMaxS( weights, DBL_MIN, weights );
if( is_spherical )
{
cvLog( log_det, log_det );
cvScale( log_det, log_det, dims );
}
} // end of iteration process
//log_weight_div_det[k] = -2*log(weights_k/det(Sigma_k))^0.5) = -2*log(weights_k) + log(det(Sigma_k)))
if( log_weight_div_det )
{
cvScale( log_weights, log_weight_div_det, -2 );
cvAdd( log_weight_div_det, log_det, log_weight_div_det );
}
/* Now finalize all the covariation matrices:
1) if <cov_mat_type> == COV_MAT_DIAGONAL we used array of <w> as diagonals.
Now w[k] should be copied back to the diagonals of covs[k];
2) if <cov_mat_type> == COV_MAT_SPHERICAL we used the 0-th element of w[k]
as an average variation in each cluster. The value of the 0-th element of w[k]
should be copied to the all of the diagonal elements of covs[k]. */
if( is_spherical )
{
for( k = 0; k < nclusters; k++ )
cvSetIdentity( covs[k], cvScalar(cov_eigen_values->data.db[k]));
}
else if( is_diagonal )
{
for( k = 0; k < nclusters; k++ )
cvTranspose( cvGetRow( cov_eigen_values, &whdr, k ),
cvGetDiag( covs[k], &diag ));
}
cvDiv( 0, cov_eigen_values, inv_eigen_values );
log_likelihood = _log_likelihood;
__END__;
cvReleaseMat( &log_det );
cvReleaseMat( &log_weights );
cvReleaseMat( &covs_item );
cvReleaseMat( &centered_sample );
cvReleaseMat( &cov_eigen_values );
cvReleaseMat( &samples );
cvReleaseMat( &sum_probs );
return log_likelihood;
}
int CvEM::get_nclusters() const
{
return params.nclusters;
}
const CvMat* CvEM::get_means() const
{
return means;
}
const CvMat** CvEM::get_covs() const
{
return (const CvMat**)covs;
}
const CvMat* CvEM::get_weights() const
{
return weights;
}
const CvMat* CvEM::get_probs() const
{
return probs;
}
using namespace cv;
CvEM::CvEM( const Mat& samples, const Mat& sample_idx, CvEMParams params )
{
means = weights = probs = inv_eigen_values = log_weight_div_det = 0;
covs = cov_rotate_mats = 0;
// just invoke the train() method
train(samples, sample_idx, params);
}
bool CvEM::train( const Mat& _samples, const Mat& _sample_idx,
CvEMParams _params, Mat* _labels )
{
CvMat samples = _samples, sidx = _sample_idx, labels, *plabels = 0;
if( _labels )
{
int nsamples = sidx.data.ptr ? sidx.rows : samples.rows;
if( !(_labels->data && _labels->type() == CV_32SC1 &&
(_labels->cols == 1 || _labels->rows == 1) &&
_labels->cols + _labels->rows - 1 == nsamples) )
_labels->create(nsamples, 1, CV_32SC1);
plabels = &(labels = *_labels);
}
return train(&samples, sidx.data.ptr ? &sidx : 0, _params, plabels);
}
float
CvEM::predict( const Mat& _sample, Mat* _probs ) const
{
CvMat sample = _sample, probs, *pprobs = 0;
if( _probs )
{
int nclusters = params.nclusters;
if(!(_probs->data && (_probs->type() == CV_32F || _probs->type()==CV_64F) &&
(_probs->cols == 1 || _probs->rows == 1) &&
_probs->cols + _probs->rows - 1 == nclusters))
_probs->create(nclusters, 1, _sample.type());
pprobs = &(probs = *_probs);
}
return predict(&sample, pprobs);
}
int CvEM::getNClusters() const
{
return params.nclusters;
}
Mat CvEM::getMeans() const
{
return Mat(means);
}
void CvEM::getCovs(vector<Mat>& _covs) const
{
int i, n = params.nclusters;
_covs.resize(n);
for( i = 0; i < n; i++ )
Mat(covs[i]).copyTo(_covs[i]);
}
Mat CvEM::getWeights() const
{
return Mat(weights);
}
Mat CvEM::getProbs() const
{
return Mat(probs);
}
/* End of file. */